Void Volume Considerations

This suggests that there is no actual penetration of the eluent and also the analyte molecules between the bonded ligands, but rather the accumulation (adsorption) of them on the surface. This was also confirmed by the study of the viscosity of bonded chains [32], which shows that the viscosity of bonded C18-type alkyl chains is at least two orders of magnitude higher than the viscosity of corresponding free alkanes (note that free octadecane is solid at room temperature, and it is almost insoluble in acetonitrile). 

Void volume is a critical parameter in HPLC, since most theoretical relationships in chromatographic theory deal with the retention factor, and the accuracy of the void volume determination plays an important role in all calculations. 

The concept of the void volume and mobile-phase volume was briefly discussed in Chapter 1, Section 1.7.2. In the partitioning model (Section 2.8) the total volume of the liquid phase in the column is equal to the sum of the volumes of the mobile and stationary phase in the same column. 

Adsorption model of HPLC retention mechanism allows clear definition of the column void volume as the total volume of the liquid phase in the column, but this model requires the use of the surface-specific retention and the correlation of the HPLC retention with the thermodynamic (and thus energetic) parameters, which is not well-developed. This model requires the selection of the standard state of given chromatographic system and relation of all parameters to that state. 

In most analytical applications of HPLC, all these discrepancies are quietly and conveniently forgotten, and selection of some so-called nonretained component as a void volume marker is a common way for void volume measurement. In the majority of recent analytical publications, either thiourea or uracil were used as the void volume markers. As a disclaimer, we have to say here that for the purposes of analytical method development, qualitative or quantitative separation of complex mixtures which involves the use of a nonretained component as a void volume marker is acceptable insofar as there are no physicochemical generalization, thermodynamic development, or futher theoretical development performed upon the basis of these pseudo void volume determinations. 

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A considerable amount of information has been reported regarding mass transfer between a single fluid phase and solid particles (such as those of spherical and cylindrical shape) forming a fixed bed. A recent review has been presented by Norman (N2). The applicability of such data to calculations regarding trickle-flow processes is, however, questionable, due to the fundamental difference between the liquid flow pattern of a fixed bed with trickle flow and that of a fixed bed in which the entire void volume is occupied by one fluid. 

We will start by developing an expression for the average pore radius T. If we denote the mass of an individual catalyst particle by raP, simple geometric considerations indicate that the void volume per particle is given by... 

A piperidene-based intermediate was found to crystallize as either an anhydrate or a hydrate, but the impurity profile of the crystallized solids differed substantially [26], Considerations of molecular packing led to the deduction that there was more void volume in the anhydrate crystal structure than in that of the hydrate form, thereby facilitating more clathration in the anhydrate than in the hydrate phase. This phenomenon was led to a decision to crystallize the hydrate form, since lower levels of the undesired impurity could be occluded and greater compound purity could be achieved in the crystallization step. 

Wallis points out that, from continuity considerations and bubble dynamics, the cocurrent flow of uniformly dispersed bubbles as a discontinuous phase in a liquid can always be made to occur in any system and for any void volume. (This is not true for countercurrent flow.) Coalescence of bubbles may occur, of course, and if this coalescence is sufiiciently rapid, a developing type of flow is observed, usually from bubble to slug flow. Because of this behavior, the particular flow pattern observed in bubble flow is quite dependent on the previous history of the two-phase mixture. This would be true for both horizontal and vertical flow. 

It is of interest to relate the void volume as calculated from water adsorption volume to the framework density of the zeolites—i.e., the density of the zeolite structure with no consideration of the nonframework atoms (cations and water). The framework density may be expressed in terms of grams per cubic centimeter or in terms of the number of tetrahedra per unit volume of 1000 A3. A plot of the framework density for zeolites of known structure vs. the void fraction, Vf, as determined from water... 

The volume of the NMR detection cell is relatively large (30-240 xl) when compared with the peak volumes and other void volumes in the chromatographic system. This leads to a considerable broadening of the peaks when they pass the NMR detection cell. It takes a long time until a peak is completely washed out of the flow cell, i.e. a tailing is observed. This is especially critical when traces of a high-concentration first peak interferes with the spectrum of a minor compound. 

The sulfur sorbent that has received the most attention is limestone because of its widespread availability and low cost. Unfortunately the conversion of limestone to calcium sulfate results in a volumetric increase, and it can be readily shown (8 ) that for particles that do not permit volumetric expansion on reaction the maximum conversion attainable is about 59 percent (the value is dependent on the specific volumes of reactant and product). This constraint can be avoided by use of dolomite, since the MgO is not sulfated and the void volume produced by the decomposition of MgCO and CaCO is sufficient to permit complete calcium utilization, but at the expense of an added weight of sorbent and added energy requirement for calcination. The above conclusions follow from consideration of the stoichiometric relations ... 

If we disengage ourselves from the consideration of mobile and stationary phases and assume (as a very rough approximation) that column void volume is the volume of the mobile phase = Yo) and leave stationary-phase volume... 

Maintain geometrical similarity as much as reasonably possible. From practical procurement considerations, the smallest (about 1/8" for the HEM), least expensive, and most readily available mixers have relatively shorter elements (Le/D < 1) and lower void volumes (VF < 0.8) whereas plant-size units have relatively longer elements (Le/D ks 1.5) and larger void volume fractions (VF = 0.9). Thus, if needed, scale-up may be accomplished by breaking geometrical similarity, but deviate only as needed. 

Permeability. Although wood is a porous material (60—70% void volume), its permeability (ie, flow of liquids under pressure) is extremely variable. This is due to the highly anisotropic shape and arrangement of the component cells and to the variable condition of the microscopic channels between cells. In the longitudinal direction, the permeability is 50 to 100 times greater than in the transverse direction (13). Sapwood is considerably more permeable than heartwood. In many instances, the permeability of the heartwood is practically zero. A rough comparison, however, may be made on the basis of heartwood permeability, as shown in Table 3. 

Another consideration in efficient elution with an organic solvent is removal of water from the C-18 sorbent. In order for the elution solvent to effectively wet the bed of the sorbent, it is necessary that both water in the void volume, trapped water, and water sorbed to the silica be removed. 

The constrained geometry of the inner void volume of zeolites, and particularly of mesoporous materials, provides an important space of nanodimensions for accommodation of large molecules. It is expected that flexible polymers synthesized in the conditions of constrained geometry could exhibit different properties compared to nonconstrained systems. Considerable effort has been exerted to synthesize conducting polymers by polymerization of the respective monomers in the presence of zeolites ion-exchanged with some transition metals. 

Dendrimers have attracted considerable attention in the polymer field over the past two decades as they have been recognized as the most important macromolecules possessing tunable internal packing density, void volumes, solvent-dependent size, branching dimensions, and surface functionalities. Since the first report of a dendrimer-like molecule in 1978 [33], significant progress has been made in the dendrimer chemistry. A large number of dendrimer compositions (families) and dendrimer surface modifications have been reported. A plethora of applications related to controlled release of pharmaceuticals have been reported. Currently, there are two widely studied dendrimer families, namely the Tomalia-type polyamidoamine (PAMAM) dendrimers and the Frdchet-type polyether dendrimers. PAMAM dendrimers are the first complete dendrimer family to have been synthesized. 

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